Combinations-ISI 2004

[kangkan]

Is there a fromula to do this that doesnt involve manual counting?

.5 boys and 4 girls are to seated ina row so that no girl sit together..apparently the ans is 6P4* 5!

:)

[Homer Simpson]

What is the logic of the formula?

[The Villain]

no formula..its very easy...just think
first make the boys sit
*B*B*B*B*B*B*
Now there are 6 gaps depicted by *...the girls can be seated in 6P4 ways :))
So total 5!*6P4

[kangkan]

but ron even G BB G B G B G B is an acceptable arrangement...we left that out :(

[L14]

Hi Kangkan that combination you've mentioned is also included in the soln that ron had posted
imagine the 6 *s are filled by only 4 girls, so the combinations will be like
GBGBGBGBB
GBGBGBBGB
GBGBGBBBG..etc
and the combination you've mentioned will also come under this.
There will be 6C4 such combinations. Since all the girls are distinct, the possible arrangements keeping the boys fixed are 6P4. And the boys can be arranged among themselves in 5! ways. so 6P4*5!

[The Villain]

Kangkan...its already included as Ben pointed out

[kangkan]

ye yes..got it :)